The check valve in my water pump has begun to leak intermittently. When it does, water flows from the city water connection through the pump into the fresh water tank, eventually overfilling it and causing it to overflow onto the ground.

I know I can fix this by placing a check valve 'in front' of the water pump.

I always use a filter when connected to city water and when filling the fresh water tank so I don't think it is a matter of sediment interfering with the check valve built in to the pump. I also have an external pressure regulator in addition to the one built in to the plumbing so I don't think it is an over pressure condition.

My question is whether I should suspect a immanent pump failure?

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Take the head off the pump and you should find a 4 valve rotor pump. You should be able to lift the valve off and see if there is dirt under it or if the rubber has failed. Not sure if parts are available.

The pump head is the check valve. If one of the valves is bad that is the one that is leaking. Depending on which valve is closed when you shut off the pump will determine if it leaks back to the tank.